If $$A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] $$, then $$A^{2}-4\ A$$ is equal to

If $$A$$ and $$B$$ are square matrices such that $$B=-A^{-1}BA$$, then 

If $$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{matrix} \right] $$ and $$10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha  \\ 1 & -2 & 3 \end{matrix} \right] $$ where $$B=A^{-1}$$ then $$\alpha$$ is equal to-

The inverse of the matrix  $$\left[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 3 } & { 3 } & { 0 } \\ { 5 } & { 2 } & { - 1 } \end{array} \right]$$  is

If $$A$$ is a $$2\times 2$$ matrix such that $$A^{2}-4A+3I=0$$, then the inverse of $$A+3I$$ is equal to

Let A be a $$3\times 3$$ matrix such that
$$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix} \right] =\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix} \right] $$  Then $${ A }^{ -1 }$$.

Inverse of $$\begin{bmatrix} -1 & 5 \\ -3 & 2 \end{bmatrix}$$ is

If $$A=\left[ \begin{matrix} cos\theta  & -sin\theta  \\ sin\theta  & cos\theta  \end{matrix} \right] { A }^{ 1 }$$ is given by:

If $$\begin{bmatrix} 1 & -\tan { \theta  }  \\ \tan { \theta  }  & 1 \end{bmatrix}{ \begin{bmatrix} 1 & -\tan { \theta  }  \\ \tan { \theta  }  & 1 \end{bmatrix} }^{ -1 }={ \begin{bmatrix} \cos { \alpha  }  & -\sin { \alpha  }  \\ \sin { \alpha  }  & \cos { \alpha  }  \end{bmatrix} }^{ -1 }$$, then $$\alpha $$=

A is a $$2\times 2$$ matrix such that $$A\begin{bmatrix} 1 &  \\  & -1 \end{bmatrix}=\begin{bmatrix} 1 &  \\ 0 &  \end{bmatrix}$$ and $${ A }^{ 2 }\begin{bmatrix} 1 &  \\  & -1 \end{bmatrix}=\begin{bmatrix} 1 &  \\ 0 &  \end{bmatrix}$$. The sum of the elements f A, is

Let A be a $$3 \times 3$$  matrix such that is: $$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix} \right]  $$Then $$A^{-1}$$ is

If $$A=[x \quad y],B=[_{ h } ^{ a }\quad _{ b } ^{ h }],C=[_{ y } ^{ x }]$$, then $$ABC = $$ ___.

If $$A=\begin{bmatrix} \alpha  & 0 \\ 1 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$$ then the value of $$\alpha $$ for which $$A^2=b$$ is

If a , b and c are all different from zero such that $$\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 0$$, then the matrix A = $$\begin{vmatrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{vmatrix}$$ is - 

If $$\displaystyle \begin{bmatrix} a & b \\ -a & 2b \end{bmatrix}\left[ \begin{matrix} 2 \\ -1 \end{matrix} \right] =\left[ \begin{matrix} 5 \\ 4 \end{matrix} \right] $$ then $$(a,b)$$ is

Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?

For each real $$ x, -1 < x < 1 . $$ let A (x) be the matrix $$(1-x)^{-1} \begin{bmatrix} 1 & -x \\ -x & 1 \end{bmatrix} $$ and  z  = $$ \dfrac { x +y }{ 1 +xy} $$. then